Explicit construction of infinite families of strongly regular digraphs with parameters $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, \lambda, t)$

An explicit construction of infinite sequences of strongly regular graphs with parameter sets $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, \lambda, t)$ is described. A computer program was used to find the initial digraphs. The remaining terms of the sequence are obtained automatically by the constructed recurrent algorithm. Using the described approach, $11$ families of strongly regular graphs have been found. In particular, these families contain digraphs $\text{dsrg}(40, 10, 3, 1, 3)$, $\text{dsrg}(72, 18, 5, 3, 5)$, $\text{dsrg}(76, 19, 5, 4, 5)$, $\text{dsrg}(92, 23, 6, 5, 6)$ and $\text{dsrg}(104, 26, 7, 5, 7)$, the question of the existence of which was previously open.